In this paper, we investigated brain network changes during AD progression by using new brain network topological metrics that are different from the conventional cost-efficiency methods. We did not only rely on the shortest paths (Fig. REF a) but also the less investigated ([1]}), alternative (or parallel, see a toy example in Fig. REF b) paths between each pair of nodes. For example, a magnetoencephalography (MEG)-based FC study defined various redundancy metrics at each frequency band and found that the brain functional network express more redundancy than the random network ([1]}). They further calculated an average number of alternative paths in an electroencephalogram (EEG)-based FC network in the entire network of spinal cord injured patients as a global measurement of redundancy but did not find any significant changes compared to the healthy subjects ([3]}). In an AD vs. control study, education level was found to act as a cognitive reserve by strengthening the redundancy of a partial brain network constructed by using diffusion MRI ([4]}). The inclusion of redundant paths can imply different aspects to the brain connectome, which is further summarized as different types of efficiency, together describing trade-offs among efficiency, cost, and resilience ([5]}). Different from these previous studies, we proposed an intuitive and easy-to-calculate metric describing whether there are always other paths in addition to the shortest path for every pair of nodes. Such a redundancy design in other natural networks has been consistently found and studied ([6]}, [7]}, [8]}). We hereby analyzed much denser brain networks by also including weak edges, where the backup routes will likely emerge and the redundancy could become the dominant theme compared to cost efficiency.
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